These words are used interchangeably and most times used incorrectly. Are you referring to chemical straighteners? Temporary products that help smooth the hair for 24 hours? Products that coat the cuticle with the sealing of a flat iron?
Chemical straighteners/relaxers are products that chemically rearrange the bonds of the hair causing a chemical permanent change. A few technical terms that describe chemical straighteners/relaxers are sodium hydroxide, calcium hydroxide or ammonium thioglycolate. These chemicals rearrange the internal bonds of the hair.
The words smoothing treatments refer to temporarily relaxing the hair for more than a blow dry service and with the help of the treatment the hair is manageable for 60 washes or more.
Hope this helps, I am here to help you learn and correct more issues with your hair.